Center vortices and confinement vs. screening

TL;DR

This paper investigates how center vortices influence confinement and screening in SU(N) gauge theories, constructing models in two dimensions and analyzing Wilson loops for fundamental and adjoint representations, revealing confinement, screening, and universal potential behaviors.

Contribution

The paper develops a center-vortex model in two dimensions for arbitrary N, demonstrating confinement and screening, and extends the analysis to adjoint Wilson loops, highlighting universal potential forms and limitations of dilute vortex approximations.

Findings

Confinement observed in the constructed 2D vortex model.

Screening occurs in the adjoint Wilson-loop potential.

Universal form of the adjoint potential independent of N at fixed K_F.

Abstract

We study adjoint and fundamental Wilson loops in the center-vortex picture of confinement, for gauge group SU(N) with general N. There are N-1 distinct vortices, whose properties, including collective coordinates and actions, we study. In d=2 we construct a center-vortex model by hand so that it has a smooth large-N limit of fundamental-representation Wilson loops and find, as expected, confinement. Extending an earlier work by the author, we construct the adjoint Wilson-loop potential in this d=2 model for all N, as an expansion in powers of $\rho/M^2$, where $\rho$ is the vortex density per unit area and M is the vortex inverse size, and find, as expected, screening. The leading term of the adjoint potential shows a roughly linear regime followed by string breaking when the potential energy is about 2M. This leading potential is a universal (N-independent at fixed fundamental string tension $K_F$) of the form $(K_F/M)U(MR)$, where R is the spacelike dimension of a rectangular Wilson loop. The linear-regime slope is not necessarily related to $K_F$ by Casimir scaling. We show that in d=2 the dilute vortex model is essentially equivalent to true d=2 QCD, but that this is not so for adjoint representations; arguments to the contrary are based on illegal cumulant expansions which fail to represent the necessary periodicity of the Wilson loop in the vortex flux. Most of our arguments are expected to hold in d=3,4 also.